Triangle abc has vertices a (0,10) b (4,10) and c (-2,4) find the orthocenter of triangle abc

Hence the orthocenter is (-2,12)

Step-by-step explanation:

We need to find the Orthocenter of ΔABC with vertices A(0,10) , B(4,10) and C(-2,4).

" Orthocenter of a triangle is a point of intersection, where three altitudes of a triangle connect ".

Step 1 :  Find the perpendicular slopes of any two sides of the triangle.  

Step 2 : Then by using point slope form, calculate the equation for those two altitudes with their respective coordinates.

Step 1 :  Given coordinates are: A(0,10) , B(4,10) and C(-2,4)

Slope of BC =

Perpendicular Slope of BC = -1

( since for two perpendicular lines the slope is given as:

where   are the slope of the two lines. )

Slope of AC =

Perpendicular Slope of AC=

Step 2 :  Equation of AD, slope(m) = -1 and point A = (0,10)

Equation of BE, slope(m) =\dfrac{-1}{3} and point B = (4,10)

----------(2)

Solving equations (1) and (2), we get

(x, y) = (-2,12)

Hence, the orthocenter is (-2,12).

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step-by-step explanation: